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Area Preserving Transformations in Non-commutative Space and NCCS Theory

M. Eliashvili·G. Tsitsishvili
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Abstract

We propose an heuristic rule for the area transformation on the non-commutative plane. The non-commutative area preserving transformations are quantum deformation of the classical symplectic diffeomorphisms. Area preservation condition is formulated as a field equation in the non-commutative Chern-Simons gauge theory. The higher dimensional generalization is suggested and the corresponding algebraic structure - the infinite dimensional $\sin$-Lie algebra is extracted. As an illustrative example the second-quantized formulation for electrons in the lowest Landau level is considered.

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M. Eliashvili, G. Tsitsishvili. 2003-06-29. Area Preserving Transformations in Non-commutative Space and NCCS Theory. https://doi.org/10.1140/epjc%2Fs2003-01373-3

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